Question

Q35)A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that

of a red ball, determine the number of blue balls in the bag.​

Answer 1

$\bf\underline{\underline{\orange{SOLUTION:-}}}$

Question

• A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, determine the number of blue balls in the bag?

Answer

• Number of balls in the bag = 10

Given

• In bag 5 red balls
• P(B) =2P(R)

To Calculate

• Number of balls in the bag __?

Step by Step Explanation

Let the number of blue balls in the bag = x

Total Number of balls in the bag = 5+x

Probability of drawing a blue ball

$⇝ \: \frac{Number \: of \: blue \: balls }{Total \: Number \: of \: balls }$

P(B) = x/5+x

Probability of drawing a red balls

$⇝ \: \frac{Number \: of \: red \: balls }{Total \: Number \: of \: balls }$

P(R) = 5/5+x

$\bf\underline{\underline{\red{Given:-}}}$

P(B) = 2P(R)

$\frac{x}{5 + x} =2( \frac{5}{5 + x} )$

$⇢ \: \frac{x}{5 + x} = \frac{10}{5 + x}$

⇢ 10(5+x)= x(5+x)

⇢ 50+10x=5x+x²

⇢ x²+5x-10x-50=0

⇢ x²-5x-50=0

⇢ x²-(10-5)x-50=0

⇢ x²-10x+5x-50=0

⇢ x(x-10)+5(x-10)=0

⇢ (x-10)(x+5)=0

⇢ x-10=0,x+5=0

⇢ x=10,x=-5(neg.)

x=10

$\bf\underline{\underline{\</strong><strong>orange</strong><strong>{</strong><strong>HENCE</strong><strong>:-}}}$

• Number of balls in the bag = 10

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Answer 2

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